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Machine Elements II (EXAMPLES – )

EXAMPLES – GEARS

Example 1: Shilds p. 76 A 20° full depth spur is to trans­mit 1.25 kW at 850 rpm. The pinion has 18 teeth. Determine the Lewis bending stress if the module is 2 and the face width is 25 mm.

Example 2: Shilds p. 81 A speed reducer has a 22-tooth spur pinion made of steel, driving a 60-tooth made of cast iron. The transmitted power is 10 kW. The pinion speed is 1200 rpm, module 4 and face width 50 mm. Determine the contact stress.

Example 3: Shilds p. 92 A spur pinion has a module of 2.5 and 18 teeth cut on the 20° full depth system and is to trans­mit 4kW power at 1100rpm. Using the Lewis formula, determine the resulting bending stress if the face width is 30 mm.

Example 4: Shilds p. 92 A 20° full depth spur pinion is to transmit 1.75kW at 1200rpm. If the pinion has 18 teeth with a module of 2, determine a suitable value for the face width, based on the Lewis formula, if the bending stress should not exceed 75 MPa.

Example 5: Shilds p. 93 Using the Lewis formula, estimate the power rating of a 20° full depth spur pinion having a module of 6, 21 teeth and face width 50 mm, if the maximum bending stress is 117 MPa. The design speed is 850 rpm.

Example 6: Shilds p. 93 A 20-tooth, 20° pressure angle, module 4 cast iron spur pinion is used to drive a 32-tooth cast iron gear. Using equation 4.13, determine the contact stress if 10.5 kW is transmitted. The pinion speed is 950 rpm and the face width is 50 mm.

page 1 AMEM 317: Elements II (EXAMPLES – SPRINGS) EXAMPLES – SPRINGS

Example 1: (Shigley Book, 10-1, page 604) A helical compression spring is made of music wire (d=0.94 mm). The outside diameter of the spring is 11 mm. The ends are squared and there are 12.5 total turns. (a) Estimate the torsional yield strength of the wire. (b) Estimate the static load corresponding to the yield strength. (c) Estimate the spring rate. (d) Estimate the deflection that would be caused by the load in part (b). (e) Estimate the solid length of the spring. (f) What length should the spring be to ensure that when it is compressed solid and then released, there will be no permanent change in the free length? (g) Given the length found in part (f), is buckling a possibility? (h) What is the pitch of the body coil?

Example 2: (Shigley Book, 10-2, page 611) A music wire helical compression spring is needed to support a 89 N load after being compressed 50 mm. Because of assembly considerations the solid height cannot exceed 25 mm and the free length cannot be more than 100 mm. Design the spring.

Example 3: (Shigley Book, 10-3, page 613) Indexing is used in machine operations when a circular part being manufactured must be divided into a certain number of segments. Fig. 1 shows a portion of an indexing fixture used to successively position a part for the operation. When the knob is pulled up, part 6, which holds the workpiece, is rotated to the next position and locked in place by releasing the index pin. In this example we wish to design the spring to exert a force of about 14 N and to fit in the space defined in the figure caption.

Part 1, pull knob; Part 2, tapered retaining pin; Part 3, hardened bushing with press fit; Part 4, body of fixture; Part 5, indexing pin; Part 6, workpiece holder. Space of the spring is 16 mm OD, 6.25 mm ID, and 35 mm long, with the pin down as shown. The pull knob must be raised 19 mm to permit indexing.

Fig. 1

Example 4: (Shigley Book, 10-5, page 623) An as-wound helical compression spring, made of music wire, has a wire size of 2.3 mm, an outside coil diameter of 14 mm, a free length of 110 mm, 21 active coils, and both ends squared and ground. The spring is unpeened. This spring is to be assembled with a preload of 22N and will operate with a maximum load of 156N during use. (a) Estimate the factor of safety guarding against fatigue failure using a torsional Gerber fatigue failure. (b) Estimate the critical frequency of the spring.

Example 5: (Shigley Book, 10-7, page 632) Consider an unpeened music wire helical coil compression spring formed with 1.0 mm wire with squared and ground ends, and with the following dimensions and characteristics. The helix diameter D is 8.0 mm, the free length Lo is 20.5 mm, the solid height Ls is 8.0 mm, intended to be flexed between Lmin = 10 mm and Lmax = 17.5 mm, and wound with 8 total turns. Estimate the fatigue cycles to failure Nf using a Gerber failure locus using Associated Spring data.

page 2 Machine Elements II (EXAMPLES – )

CLUTCHES EXAMPLES AND WORKSHEET (Mechanical Design, P. Childs)

A. EXAMPLES

Example 1: A is required for of power between a four-cylinder internal combustion engine and a small machine. Determine the radial dimensions for a single dry disc clutch with a moulded lining which should transmit 5kW at 1800rpm. Consider that the wear is uniform.

Example 2: A multiple disc clutch, running in oil, is required for a with a three-cylinder engine. The power demand is 75 kW at 8500 rpm. The preliminary design layout indicates that the maximum diameter of the clutch discs should not exceed 100 mm. In addition, previous designs have indicated that a moulded lining with coefficient of friction of 0.068 in oil and a maximum permissible pressure of 1.2 MPa is reliable. Within these specifications determine the radii for the discs, the number of discs required and the clamping force.

B. WORKSHEET

1. Calculate the torque a clutch must transmit to accelerate a with a moment of inertia of 0.25 kgm2 to: (a) 500rpm in 2.5s, (b) 1000rpm in 2s. 2. Calculate the energy that must be absorbed in stopping a 100 tone airbus traveling at 250 km/h in an aborted takes off stopping in 40 s. 3. A disc clutch has a single pair of mating surfaces of 300 mm outside diameter and 200 mm inner diameter. If the coefficient of friction is 0.3 and the actuating force is 4000 N, determine the torque capacity assuming: (a) uniform wear, (b) uniform pressure. 4. A multiple disc clutch running in oil is required for a touring motorcycle. The power demand is 75 kW at 9000 rpm. Space limitations restrict the maximum outer diameter of the clutch plates to 200 mm. Select an appropriate lining material and determine the radii for the discs, the number of discs required and the clamping force. 5. A multiple disc clutch is required for a high-performance motorcycle. The power demand is 100 kW at 12 000 rpm. Select an appropriate lining material and determine the radii for the discs, the number of discs required and the clamping force. 6. A multiple disc clutch is required for a small motorcycle. The power demand is 9 kW at 8500 rpm. Select an appropriate lining material and determine the radii for the discs, the number of discs required and the clamping force.

page 3 Machine Elements II (EXAMPLES – BRAKES) BRAKES EXAMPLES AND WORKSHEET (Mechanical Design, P. Childs)

A. EXAMPLES

Example 1: A caliper brake is required for the front of a sports with a braking capacity of 820Nm for each brake. Preliminary design estimates have set the brake geometry as r1=100mm, ro=160mm and θ=45°. A pad with a coefficient of friction of 0.35 has been selected. Determine the required actuating force and the average and maximum contact pressures.

Example 2: Design a long-shoe to produce a friction torque of 75Nm, to stop a drum rotating at 140rpm. Initial design calculations have indicated that a shoe lining with μ=0.25, and using a value of pmax =0.5x106 N/m2 in the design, will give suitable life.

Example 3: For the double long-shoe external drum brake illustrated in Fig. 7.14, determine the limiting force on the lever such that the maximum pressure on the does not exceed 1.4MPa, and determine the torque capacity of the brake. The face width of the shoes is 30mm and the coefficient of friction between the shoes and the drum can be taken as 0.28.

Fig. 7.14: Double long-shoe external drum brake

page 4 Machine Elements II (EXAMPLES – BRAKES)

Example 4: Determine the actuating force and the braking capacity for the double internal long-shoe brake, illustrated in Fig. 7.17. The lining is sintered metal with a coefficient of friction of 0.32, and the maximum lining pressure is 1.2 MPa. The drum radius is 68 mm and the shoe width is 25 mm.

Example 5: Design a band brake to exert a braking torque of 85 Nm. Assume the coefficient of friction for the lining material is 0.25 and the maximum permissible pressure is 0.345MPa (a=80mm, c=150mm).

page 5 Machine Elements II (EXAMPLES – BRAKES)

B. WORKSHEET

1. A caliper brake is required for the front wheels of a passenger car with a braking capacity of 320N-m for each brake. Preliminary design estimates have set the brake geometry as ri=

100mm, r0 = 140mm and θ= 40°. Pads with a coefficient of friction of 0.35 have been selected. Each pad is actuated by means of a hydraulic cylinder of nominal diameter 25.4mm. Determine the required actuating force, the average and the maximum contact pressures, and the required hydraulic pressure for brake actuation. 2. Determine the torque capacity for the single short-shoe brake shown in Fig. 7.20. The coefficient of friction is 0.35.

3. The maximum actuating force on the double short-shoe external drum brake illustrated in Fig. 7.21 is 1 kN. If the coefficient of friction for the shoe lining is 0.3, determine the torque Capacity of the brake for clockwise rotation.

page 6 Machine Elements II (EXAMPLES – BRAKES)

4. A double short-shoe external brake is illustrated in Fig. 7.22. The required actuating force to limit the drum rotation to 100 rpm is 2.4 kN. The coefficient of friction for the brake lining is 0.35. Determine the braking torque and the rate of heat generation.

5. The single long-shoe external brake illustrated in Fig. 7.23 operates on a drum of diameter 300 mm. The coefficient of friction for the brake lining is 0.3 and the face width of the shoes is 40 mm. If the actuating force is 500 N, determine the maximum shoe pressure and the braking torque.

page 7 Machine Elements II (EXAMPLES – BRAKES)

6. A double long-shoe external drum brake is illustrated in Fig. 7.24. The face width of the shoes is 50 mm and the maximum permissible lining pressure is 1 MPa. If the coefficient of friction is 0.32, determine the limiting actuating force and the torque capacity.

7. The double long-shoe internal drum brake illustrated in Fig. 7.25 has a shoe outer diameter of 280 mm and shoe width of 40 mm. Each shoe is actuated by a force of 2kN. The coefficient of friction for the brake lining is 0.25. Find the magnitude of the maximum pressure and the braking torque.

page 8 Machine Elements II (EXAMPLES – BRAKES)

8. A double long-shoe internal brake as illustrated in Fig. 7.26 has a diameter of 200 and a shoe face width of 30 mm. The coefficient of friction for the brake lining is 0.4 and the maximum permissible stress is 1.2 MPa. Each brake shoe is actuated by equal forces. Determine what the value is for the actuating force on each shoe and determine the torque capacity for the brake.

15. A simple band brake is shown in Fig. 7.27. The maximum permissible pressure for the brake lining is 0.6 MPa. The brake band is 100 mm wide and has a coefficient of friction of 0.3. The angle of contact between the band and the drum is 270°. Determine the tensions in the brake band and the torque capacity if the drum diameter is 0.36 m.

page 9 Machine Elements II (EXAMPLES – BRAKES)

page 10 AMEM 317: Machine Elements II (EXAMPLES – AND CHAIN DRIVES)

BELT AND CHAIN DRIVES EXAMPLES (Mechanical Design, P. Childs)

A. BELT DRIVES EXAMPLES

Example 1:

Select a wedge belt and determine the pulley diameters for a reciprocating compressor driven by a 28 kW two-cylinder . The engine speed is 1500 rpm and the compressor speed is 950 rpm. The proposed distance between the engine and compressor shaft centres is approximately 1.5 m. The system is expected to be used for less than 10 hours per day.

Example 2:

A fan is belt driven by an running at 1500rpm. The pulley diameters for the fan and motor are 500 mm and 355 mm respectively. A flat belt has been selected with a width of 100 mm, thickness of 3.5 mm, coefficient of friction of 0.8, density of 1100kg/m3 and permissible stress of 11MN/m2 (11MPa). The centre distance is 1500 mm. Determine the power capacity of the belt.

WORKSHEET

1. A four-cylinder diesel engine running at 2000 rpm, developing 45 kW, is being used to drive a medium duty agricultural machine running at 890 rpm. The distance between the pulley centres is approximately 80 cm. The expected use is less than 10 hours per day. Using a wedge belt drive, select suitable pulley diameters and determine the type and number of belts required.

2. A wedge belt drive is required to transmit 18.5 kW from an electric motor running at 1455 rpm, to a uniformly loaded conveyor running at 400 rpm. The desired centre distance is 1.4 m and expected use is 15 hours a day. Select a suitable belt, or belts, and determine the pulley diameters.

3. A wedge belt drive is required for an electric motor driven crusher. The electric motor speed and power are 720 rpm and 11 kW respectively. The desired crusher speed is 140 rpm. Limitations on space within the crushing machine restrict the use of the maximum pulley diameter to 90 cm and the pulley centre distance to less than 1 m. The device will be operated for approximately 12 hours a day. Select a suitable belt drive and pulley diameters for this application.

4. A flat belt is required to transmit 22 kW from a 250 mm diameter pulley running at 1450 rpm, to a 355 mm diameter pulley. The coefficient of friction can be taken as 0.7, the density of the belt

page 11 AMEM 317: Machine Elements II (EXAMPLES – BELT AND CHAIN DRIVES)

is 1100kg/m3 and the maximum permissible stress is 7 MPa. The distance between the shaft centres is 1.8 m. The proposed belt is 3.5mm thick. Calculate the width required.

5. A flat belt drive is required for a surface grinder to transmit 5kW from a 100 mm diameter pulley running at 1500 rpm, to a 250 mm diameter pulley. The coefficient of friction can be taken as 0.75, the density of the belt as 1100kg/m and the maximum permissible stress as 9 MPa. The distance between the shaft centres is 0.6 m. The proposed belt is 3.5 mm thick. Determine the belt width required.

6. A flat belt drive is required for a piston pump. The pump is driven by a 37 kW electric motor, running at 1470 rpm, with a pulley of 250 mm diameter. The pump pulley is 700 mm in diameter. The coefficient of friction can be taken as 0.8, the density of the belt as 1100kg/m3 and the maximum permissible stress as 6 MPa. The distance between the shaft centres is 1.2m. The proposed belt is 2.9 mm thick. Determine the belt width required.

7. The application of an existing machine has changed such that the desired transmission power has increased to 120kW. The existing design consists of a driving pulley running at 3000 rpm, with a pulley diameter of 200 mm and the driven pulley of 250 m diameter. The belt is 150 mm wide, 4.2 mm thick and has a maximum permissible stress of 6.6 MPa. The belt density and coefficient of friction are 1100kg/m3 and 0.75 respectively. The centre distance is 1.4 m. Is the belt drive suitable?

8. An extractor fan is belt driven by a 75 kW electric motor running at 2946 rpm. The pulley diameters on the fan drive and the motor drive are 300 and 200 mm respectively. The centre distance is approximately 1.4 m. Using a flat belt with a coefficient of friction of 0.8, density 1100kg/m3 and maximum permissible stress of 6 MPa, 4.3 mm thick, determine the belt width required.

page 12 AMEM 317: Machine Elements II (EXAMPLES – BELT AND CHAIN DRIVES)

B. CHAIN DRIVES EXAMPLES

Example 1:

A is required for a gear pump operating at 400 rpm, driven by a 5.5 kW electric motor running at 1440 rpm. The centre distance between the motor and pump shafts is approximately 470 mm.

WORKSHEET

1. Specify a suitable chain drive for a gear pump operating at 400 rpm, driven by a 18.5 kW electric motor running at 725 rpm. The centre distance between the motor and pump shafts is approximately 470 mm.

2. Specify a suitable chain drive for a packaging machine operating at 75 rpm, driven by a 2.2 kW electric motor running at 710 rpm. The maximum permissible centre distance between the motor and pump is 1 m.

3. Specify a suitable chain drive for a gear pump operating at 400 rpm, driven by a 30 kW electric motor running at 728 rpm. The centre distance between the motor and pump shafts is approximately 1 m.

4. Specify a suitable chain drive for a packaging machine operating at 75 rpm, driven by a 2.2 kW electric motor running at 710 rpm. The maximum permissible centre distance motor running at 2820 rpm. The centre distance between the motor and pump shafts is approximately 300 mm.

5. An agricultural application which runs for up to 16 hours per day requires a drive system to step down an 18.5 kW electric motor running at 725 rpm to 30 rpm. Determine a suitable drive system.

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